Measurement of the CKM angle ${\hat{I}}^3$ using $B^{\pm }\to D{K}^{\pm }$ with $D\to K_{\text{S}}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, $K_{\text{S}}^0{K}^{+}{K}^{-}$ decays

Abstract

A binned Dalitz plot analysis of $B^{\pm }\to D{K}^{\pm }$ decays, with $D\to K_{\text{S}}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D\to K_{\text{S}}^0{K}^{+}{K}^{-}$, is used to perform a measurement of the CP-violating observables $x_{\pm }$ and $y_{\pm }$, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle ${\hat{I}}^3$. The analysis is performed without assuming any $D$ decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0${\text{fb}}^{-1}$, the values of the CP violation parameters are found to be $x_{-}=(9.0\pm 1.7\pm 0.7\pm 0.4)\times 10^{-2}$, $y_{-}=(2.1\pm 2.2\pm 0.5\pm 1.1)\times 10^{-2}$, $x_{+}=(-7.7\pm 1.9\pm 0.7\pm 0.4)\times 10^{-2}$, and $y_{+}=(-1.0\pm 1.9\pm 0.4\pm 0.9)\times 10^{-2}$. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the strong-phase measurements. These values are used to obtain ${\hat{I}}^3={\left(87{}_{-12}^{+11}\right)}^{\circ }$, $r_B=0.086_{-0.014}^{+0.013}$, and $\hat{I}{´}_B=(101\pm 11{)}^{\circ }$, where $r_B$ is the ratio between the suppressed and favoured $B$-decay amplitudes and $\hat{I}{´}_B$ is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the \lhcb experiment, to give ${\hat{I}}^3={\left(80{}_{-9}^{+10}\right)}^{\circ }$, $r_B=0.080\pm 0.011$, and $\hat{I}{´}_B=(110\pm 10{)}^{\circ }$.

All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2018-017.html. Version 2 includes minor changes made during journal review